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Unformatted text preview: ISyE 3232 Stochastic Manufacturing and Service Systems Spring 2011 H. Ayhan & J. Dai Homework 9 March 16, 2011 (Due: at the start of class on Thursday, March 31st) 1. A Markov chain is said to be doubly stochastic if both the rows and columns of the transition matrix sum to 1. Assume that the state space is { 1 ,...,N } , and that the Markov chain is doubly stochastic and irreducible. Determine the stationary distribution . (Hint: there are two approaches. One is to solve = P and N i =1 i = 1 in general for doubly stochastic matrices. The other is to first solve a few examples, then make an educated guess about , and finally show that your guess is correct.) 2. Daily demand for paint brushes at a particular store follows the demand distribution: d 1 2 3 4 P ( D = d ) . 5 . 15 . 3 . 04 . 01 . The stock level is reviewed every evening and when warranted an order is placed at the central ware house to augment stock. Orders arrive over night and are available to meet the demand on the morninghouse to augment stock....
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 Spring '07
 Billings

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